Problem: Reduce to lowest terms: $ \dfrac{7}{5} \div \dfrac{7}{3} = {?}$
Explanation: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{7}{3}$ is $ \dfrac{3}{7}$ Therefore: $ \dfrac{7}{5} \div \dfrac{7}{3} = \dfrac{7}{5} \times \dfrac{3}{7} $ $ \phantom{ \dfrac{7}{5} \times \dfrac{3}{7}} = \dfrac{7 \times 3}{5 \times 7} $ $ \phantom{ \dfrac{7}{5} \times \dfrac{3}{7}} = \dfrac{21}{35} $ The numerator and denominator have a common divisor of $7$, so we can simplify: $ \dfrac{21}{35} = \dfrac{21 \div 7}{35 \div 7} = \dfrac{3}{5} $